COURSE GOALS
MTH 434/534

Students in MTH 434 will:

• Develop a geometric understanding of line elements and their use in describing a geometry;
• Develop a geometric understanding of selected surfaces in two and three dimensions;
• Develop the ability to multiply differential forms;
• Develop the ability to differentiate and integrate differential forms;
• Develop the ability to use differential forms to describe vector calculus;
• Develop the ability to work with both Riemannian and Lorentzian geometries in four dimensions or fewer;
• Develop the ability to compute the connection and curvature corresponding to such geometries;
• Develop an appreciation of the unifying thread brought to these topics by the use of the vector differential.

Students in MTH 534 will:

• Develop a geometric understanding of line elements and their use in describing a geometry;
• Develop a geometric understanding of selected surfaces in arbitrary dimensions;
• Develop the ability to multiply differential forms;
• Develop the ability to differentiate and integrate differential forms;
• Develop the ability to use differential forms to describe vector calculus;
• Develop the ability to work with geometries of arbitrary dimension and signature;
• Develop the ability to compute the connection and curvature corresponding to such geometries;
• Develop an appreciation of the unifying thread brought to these topics by the use of the vector differential.